Question

So sánh các lũy thừa sau:

a)\(11^{10}và121^5\)                             c)\(21^{15}và27^5.49^8\)

b)\(7.2^{13}và2^{16}\)                               d)\(3^{39}và11^{21}\)

Answer 1

a) Ta có \(121^5=\left(11^2\right)^5=11^{10}\)

Vậy \(121^5=11^{10}\)

b)Ta có \(2^{16}=2^{13}\cdot2^3=2^{13}\cdot8>7\cdot2^{13}\)

Vậy \(2^{16}>7\cdot2^{13}\)

c)  -Ta có \(21^{15}=\left(3\cdot7\right)^{15}=3^{15}\cdot7^{15}\)   (*)

     -Ta có \(27^5\cdot49^8=\left(3^3\right)^5\cdot\left(7^2\right)^8=3^{15}\cdot7^{16}\)   (**)

Từ (*) và (**) =>\(21^{15}< 27^5\cdot49^8\)

d)-Ta có: \(3^{39}=3^{38}\cdot3=\left(3^2\right)^{19}\cdot3=9^{19}\cdot3\)    (*)

   -Ta có: \(11^{21}=11^{19}\cdot11^2=11^{19}\cdot121\)    (**)

Từ (*) và (**) =>\(3^{39}< 11^{21}\)

Answer 2

a)\(121^5=\left(11^2\right)^5=11^{2.5}=11^{10}\)

\(=>11^{10}=121^5\)

Vậy \(11^{10}=121^5\)

b)Ta có :\(21^{15}=\left(3.7\right)^{15}=3^{15}.7^{15}\)

\(27^5.49^8=\left(3^3\right)^5.\left(7^2\right)^8=3^{15}.7^{16}\)

mà\(3^{15}.7^{15}< 3^{15}.7^{16}\)

\(=>21^{15}< 27^5.49^8\)

Vậy \(21^{15}< 27^5.49^8\)

c)\(7.2^{13}=7.8192=57344\)

   \(2^{16}=65536\)

mà\(57344< 65536\)

=>\(7.2^{13}< 2^{16}\)

Vậy \(7.2^{13}< 2^{16}\)

d) \(3^{39}=3^{3.13}=\left(3^{13}\right)^3=1594323^3\)

\(11^{21}=11^{7.3}=\left(11^7\right)^3=19487171^3\)

mà \(1594323< 19487171\)

\(=>3^{39}< 11^{21}\)

Vậy\(3^{39}< 11^{21}\)

  

Answer 3

a)ta có 121⁵ = (11²)⁵ = 11¹⁰.vậy...

b)ta có 2¹⁶=2³.2¹³=8.2¹³>7.2¹³

c) ta có 21¹⁵=3¹⁵.7¹⁵

            27⁵.49⁸=(3³)⁵.(7²)⁸=3¹⁵.7¹⁶>3¹⁵.7¹⁵

^{d)ko bít}

Answer 4

ngu thi ko lam duoc dau hoc ki vao